# Factor Analysis of the Aggregated Electric Vehicle Load Based on Data Mining

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Framework of Data-Mining Based Modeling

## 3. Generating Input Data by Simulation

#### 3.1. Methodology

_{i}(t) denotes the load of the i

^{th}EV (i=1,2,…,n) in time step t; and µ(t) and σ

^{2}(t) are the expectation and variance of P

_{i}(t), respectively. As long as the parameters µ(t) and σ

^{2}(t) are identified, the EV load can be predicted from Equation (1). These parameters can be calculated using the following method. When m is a large number, the law of larger number (LLN) suggests that:

_{1}(t), P

_{2}(t), …, P

_{m}(t)) (m is a large number).

#### 3.2. Simulation of the Charging Schedules

Variable Name | Variable Description |
---|---|

E_{0} | EV battery size |

R_{p} | Charging rate in public places |

R_{h} | Charging rate at home |

SOC_{m} | SOC threshold related to battery maintenance |

SOC_{a} | SOC threshold related to range anxiety |

Ρ | Penetration of public charging infrastructure |

MPGe | Miles per gallon of gasoline equivalent |

t_{up} | Instant when the price of electricity increases |

t_{down} | Instant when the price of electricity decreases |

η | Efficiency of the charger |

SOC_{0} | SOC for the first trip |

n | Total number of vehicles in the simulation |

i | EV no. |

j | Trip no. |

E | Current energy stored in the battery |

S_{i} | Total number of the trips by EV_{i} |

l_{i,j} | Mileage of trip j for EV_{i} |

_{up}and t

_{down}are the instants when the price of electricity increases and decreases, respectively. A more sophisticated TOU policy can be studied in future work. Second, the charging power is constant. The charging load of an EV is r kW, while the charging power to the battery is ηr, where r is the charging rate of the charger and η is the efficiency of the charger. Here, η = 0.9. Finally, the mileage per unit of electrical energy is 3.042 mi/kWh, which is the value for the Nissan Leaf [16].

_{m}, 1], the owner will not charge to maintain the battery. When the SOC is in the interval [0, SOC

_{a}], the owner must charge because of range anxiety. When the SOC is in the interval [SOC

_{a}, SOC

_{m}], the probability that the owner charges the EV is set as 0.5. The combination of SOC

_{m}and SOC

_{a}characterizes the owner’s charging habit.

## 4. Internal Factors Analysis

#### 4.1. Purpose and Method

_{0}, R

_{p}, R

_{h}, SOC

_{m}, SOC

_{a}, ρ); t is the time step; k is the number of factors in F, and ${\widehat{b}}_{k}$ is the coefficient estimate gained by the LR (k=0,1,…,6). Note that no TOU policy is implemented here when generating massive simulation data as input. The values of the variables can be generated randomly and the corresponding µ(F,t) can be computed by simulation. Using the same approach, models are built for workdays and weekends with separate training data.

#### 4.2. Implementation

Variable | Lower bound | Upper bound |
---|---|---|

E_{0} (kWh) ^{*} | 16 | 35 |

R_{p} (kW) ^{**} | 1.4 | 7.7 |

R_{h} (kW) | 1.4 | 7.7 |

SOC_{m} (%) | 50 | 100 |

SOC_{a} (%) | 0 | 50 |

ρ (%) | 0 | 100 |

_{p}, the coefficient ${\widehat{b}}_{k}({t}_{p})$ represents the sensitivity of the EV load to that factor. The coefficient of each factor can be used to evaluate its impact on the EV load. If the coefficient is positive, the EV load increases with the value of the factor, and vice versa. In addition, the value of the coefficient quantifies the contribution of the factor to the EV load. For instance, from 18:00 to 18:15 (the 73rd time step), the load model can be expressed as:

_{h}, if the charging rate increases 1 kW, the average EV load increases 0.0665 kW [0.419 × 1 kW/(7.7 − 1.4)] from 18:00 to 18:15.

_{p}, $\widehat{\mu}({\mathit{F}}_{p},1),\widehat{\mu}({\mathit{F}}_{p},2),\mathrm{...},\widehat{\mu}({\mathit{F}}_{p},96)$ is the estimated power demand of the EVs throughout an entire day for the specified internal factors. For example, take F

_{p}= (24, 6, 2, 90, 50, 50) (E

_{0}= 24 kWh, R

_{p}= 6 kW, R

_{h}= 2 kW, SOC

_{m}= 90%, SOC

_{a}= 50%, ρ = 50%). Figure 3 shows the results for $\widehat{\mu}({\mathit{F}}_{p},t)$ (t = 1,2,…,96), showing the real average EV load profile based on the simulation (in red) and the estimated average EV load profile from the regression Model (4) (in blue). The estimated model is accurate enough to approximate the real one.

#### 4.3. Model Validation

#### 4.4. Observations and Discussion

**Figure 4.**Stacked graphs with the regression coefficients of the internal factors. Workdays with the input data for the (

**a**) 2nd and (

**b**) 3rd travel day; Weekends with the input data for the (

**c**) 2nd and (

**d**) 3rd travel day.

#### 4.4.1. Battery Size

#### 4.4.2. Charging Rate in Public Places

_{p}significantly influences the EV load only from 7:00 to 10:30, and not 7:00 to 17:00. This phenomenon can be explained as follows. After 7:00 on workdays, many EVs arrive at workplaces from home. As travel to the workplaces consumes energy, some owners are willing to charge when EVs are parked. However, the energy demand of these EVs is not large, because most EVs start from home with a high SOC. Therefore, most EVs parking in public places can finish charging before 10:30, and so the charging rate will not significantly affect the EV load from 10:30 to 17:00.

#### 4.4.3. Charging Rate at Home

_{h}, two groups of EVs contribute to the EV load at t: the EVs that parked before t that have not finished charging and the EVs arriving at home at t to start charging (Figure 6). On the one hand, as the energy demand of the first group of EVs is limited, when R

_{h}increases, an increasing number of EVs in the first group can finish charging before t. Therefore, the power demand of the first group at t is reduced as R

_{h}increases. On the other hand, for the second group of EVs, the power demand increases with R

_{h}. It is interesting to determine how the total power demand of EVs changes with R

_{h}. Figure 4 shows that as R

_{h}increases, the EV load increases from 10:00 to 20:30 and decreases from 21:30 to 7:00. Let ∆n

_{1}(t) denote the total number of EVs that finish charging before t due to the increase in R

_{h}, and ∆n

_{2}(t) denote the total number of the EVs in the second group. It can be concluded that from 10:00 to 20:30 ∆n

_{1}is always smaller than ∆n

_{2}, while from 21:30 to 7:00, ∆n

_{1}is always greater than ∆n

_{2}. For weekends, a similar analysis can be performed.

#### 4.4.4. Battery Maintenance

_{m}shown in Figure 4, the two periods can be identified.

_{m}from 6:00 to 19:30, while the trend is opposite in the other period. A lower SOC

_{m}means caring about the battery more. Therefore, from 6:00 to 19:30 the owners charge their EVs less frequently due to battery maintenance, the approximate period that compensates for this amount of energy is from 19:30 to 6:00 the next day. According to a similar analysis, on weekends fewer EVs are charged from 6:30 to 21:00, and the “compensating” period is from 21:00 to 6:30 of the next day.

#### 4.4.5. Range Anxiety

_{a}. The higher SOC

_{a}is, the more the owner suffers range anxiety. The phenomenon shows that throughout the day, the more the owner suffers from range anxiety, the greater the power demand of the EV is, since the owners tend to keep the SOC higher. These owners can finish longer trips in their EVs, but their EVs require more energy, increasing the power demand. There is no clear difference in this phenomenon on workdays and weekends.

#### 4.4.6. Penetration of the Public Charging Infrastructure

#### 4.4.7. Critical Factors

^{th}factor is defined as:

## 5. Analysis of External Excitation

#### 5.1. Purpose and Method

_{up},t

_{down}). The estimate of µ(t) is chosen as the output of the SVR model, which is denoted as $\widehat{\mu}(t)$. As the influence of price signals is to be investigated, $\widehat{\mu}(t)$ is expanded as $\widehat{\mu}({t}_{up},{t}_{down},t)$.

_{i}, α

_{i}

^{*}and b for equation (8) (i = 1,2,…, $\ell $). An optimization problem is solved to compute the coefficients of the SVR model [22]:

_{up}, t

_{down}, t). RBF is chosen as the kernel function, and then the charging load model can be expressed as:

#### 5.2. Case Studies

_{0}(t) is the base load of the province; and L indicates the average power for a day. The meanings of the other symbols are given above.

#### 5.3. Implementation of SVR Modeling and Model Validation

_{up}, t

_{down}) is generated randomly after the values of the vector (E

_{0}, R

_{p}, R

_{h}, SOC

_{m}, SOC

_{a}, ρ) are assigned. In the case studies, the assigned value is (24, 6, 2, 90, 50, 50). Then, the corresponding µ(t

_{up}, t

_{down}, t) can be computed using the methodology in Section 3. First, 10,080 pairs of µ(t

_{up}, t

_{down}, t) and (t

_{up}, t

_{down}, t) are selected as the training set, while 4,320 pairs serve as the validation set (data for the 3rd travel day). The length of each time step is 15 minutes.

#### 5.4. Results

**Figure 9.**(

**a**) Total load for different scenarios; (

**b**) Difference between the peak and valley with different scenarios.

## 6. Conclusions

## Acknowledgments

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**MDPI and ACS Style**

Guo, Q.; Wang, Y.; Sun, H.; Li, Z.; Xin, S.; Zhang, B.
Factor Analysis of the Aggregated Electric Vehicle Load Based on Data Mining. *Energies* **2012**, *5*, 2053-2070.
https://doi.org/10.3390/en5062053

**AMA Style**

Guo Q, Wang Y, Sun H, Li Z, Xin S, Zhang B.
Factor Analysis of the Aggregated Electric Vehicle Load Based on Data Mining. *Energies*. 2012; 5(6):2053-2070.
https://doi.org/10.3390/en5062053

**Chicago/Turabian Style**

Guo, Qinglai, Yao Wang, Hongbin Sun, Zhengshuo Li, Shujun Xin, and Boming Zhang.
2012. "Factor Analysis of the Aggregated Electric Vehicle Load Based on Data Mining" *Energies* 5, no. 6: 2053-2070.
https://doi.org/10.3390/en5062053